The equation |z+1|=|z-1|, i={-1}, represents:

The line through the origin with slope 1

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UPSC NDA Math Model Paper 5

Question : 111 of 120

Marks: +1, -0

The equation

|z+1|=|z-1|, i=\sqrt{-1}

, represents:

Solution:

Given equation is: |z + 1| = |z – 1|

Let the value of ‘z’ be: z = x + iy

Now, the equation becomes,

⇒ |(x + iy) + 1| = |(x + iy)-1|

⇒ |(x + 1) + iy| = |(x – 1) + iy|

On taking modulus on both sides,

\Rightarrow \sqrt{(x+1)^2+y^2}=\sqrt{(x-1)^2+y^2}

\Rightarrow \sqrt{x^2+2x+1+y^2} = \sqrt{x^2-2x+1+y^2}

On squaring on both sides, we get

\Rightarrow x^2+2x+1+y^2 = x^2-2x+1+y^2

\Rightarrow 4x = 0

\therefore x = 0

Therefore, the equation represents y-axis.

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